The family of a murdered private detective whose killers have not been brought to justice have rejected the offer of a Scotland Yard investigation into police corruption following a meeting with the Home Secretary.

Daniel Morgan, 37, was found with an axe in his head at a south London pub car park in 1987 but the case against three men accused of killing him collapsed in March.

His brother Alastair, who has seen five inquiries into the murder fail, told Theresa May that only a judicial inquiry in public would satisfy the family.

He said he was "almost insulted" by her offer of a further police investigation, given the family's experience of forces over the past 24 years. "We made it very clear we were not interested," he said. He called the hour-long meeting with Mrs May at the Home Office a "smart piece of stonewalling".

Mr Morgan went on: "Mrs May offered another police investigation, not into the murder but into the possibility of criminality in the inquiry. We told her in no uncertain terms that we've had enough of the police." He said the family is considering "all legal options".

It is understood Mrs May urged the family to accept the offer of the police investigation but the possibility of a judge-led inquiry has still not been ruled out. No decision is expected until the end of separate inquiries by the Met and the Crown Prosecution Service.

The Home Office said: "It is deeply regrettable Daniel Morgan's killers have not been brought to justice. We understand the strength of feeling this case has caused." The family received apologies from police and lawyers in March as three men were cleared of murdering Mr Morgan, originally from Monmouthshire. Scotland Yard admitted the first inquiry into his 1987 killing was hampered by police corruption.

The outcome was even more bitter as it came on the 24th anniversary of his death in the car park of the Golden Lion in Sydenham. The five police inquiries and an inquest, as well as three years of legal hearings, are un-officially estimated at £30million.

The trial's failure hinged on the disclosure process. Amid revelations that there were crates of material defence lawyers had not been told about, the three defendants - Mr Morgan's former business partner Jonathan Rees, 54, and his brothers-in-law Garry Vian, 50, and Glenn Vian, 52 - were released.

Two other defendants - James Cook, who was accused of murder, and former Detective Sergeant Sid Fillery, charged with perverting justice - had been discharged earlier after supergrass witnesses were discredited.